2 Answers
2

For what it's worth, my iPod Touches' (2g and 3g) WiFi remains on when the screen is off, and I do get push notifications from various things (in fact, as I was typing this I got one from Ambiance). If you go out of range of known networks and "Ask to join networks" is turned on in the WiFi settings, you of course won't get push notifications unless you turn the screen on and accept an open network. The Apple battery life optimization page has a little more information, including how to control on a per-application basis what push notifications will work.

Hm? You should get a push notification; the screen will turn on, an alert will play, and a dialog will pop up. Admittedly, noticing it is sometimes a problem if it's in your pocket and you aren't wearing headphones/earbuds.
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geekosaurApr 9 '11 at 23:50

How does that relate to the Apple Support Document posted in my answer? I know my iPad's Wifi stays on too. So maybe its not correct in the Support Document even though recently updated (at least since an iPad has been out, as well as the most recent Touch I think.
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jmlumpkinApr 11 '11 at 17:40

@jmlumpkin: You'd have to ask Apple about that. I suspect that if you're using FaceTime, it would poll more often from its background hook.
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geekosaurApr 11 '11 at 18:05

This is mainly due to how Push Notifications are designed in iOS. If the device does have a connection, it will be pushed to you through Apple's servers. Because of how push works (mainly with a device checking in now and then to say 'heres where I am'), you can get push notifications while the device is asleep. The notification comes through and pushes to the device.

With iOS 4, there is also the option for developers to use local push notifications. This mainly works by just setting a designated notification at some point in the future.

Update: According to this Apple Support Document, if the screen is on, push comes on at any time. If screen is off, checks every 15 minutes.

I know all that. Push notifications requires a constant connection to Apple's servers. On devices with cellular data, it's easy since cellular are always on. However, on you don't want to have the WiFi antennas always on for battery live. The problem here is that FaceTime requires things to be fast, preferably instantaneous, so the devices cannot look at regular intervals on the server like the used to (in iOS 3.0).
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gcampApr 9 '11 at 22:15

I do not own a wifi-only device that can make FaceTime calls. I know my iPad gets push notifications with the screen off. Was just trying to answer the question with a directly link to Apple's support document. But according to the response marked as the answer, it appears that document doesn't match whats being seen.
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jmlumpkinApr 11 '11 at 17:46